Question

Show that the function f(x) = |x| is

a. strictly increasing on [0, ∞]

b. strictly decreasing on [− ∞, 0]

Answer 1

For x > 0

Modulus will open with + sign

f(x) = +x

⇒ f’(x) = +1 which is < 0

for x < 0

Modulus will open with -ve sign

f’(x) = -x = > f’(x) = -1 which is > 0

hence f(x) is increasing in x > 0 and decreasing in x < 0